I've seen a few cards eyed suspiciously, and had to explain to an operator in Europe that LA county is a real training agency so another dive could go.
I've never seen an SDI card refused, but I have never seen a diver show up with one at a remote location. Dive operators will honor cards they have heard of, but some agencies do not have a market presence in certain areas of the world. No local instruction means that the local operators may be unfamiliar with the training agency.
Example: YMCA has no instruction offered in Malta - a major dive destination for Europe. I heard of one shop there that teaches NAUI, but was not able to verify that through NAUI's website. Whether c-cards from those agencies would be honored is largely dependant on whether the dive shop staff is familiar with the agency. All it takes is one new employee running the reservation counter to refuse the card.
But if a YMCA diver obtained a CMAS card (all they need to do is send a copy of their YMCA card and check) through their equivalency program, then it should be no problem for European destinations. CMAS is widely known and recognized throughout Europe and beyond.